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Rational & Irrational Numbers Online Practice

Complete this assessment to review what you’ve learned. It will not count toward your grade.
6 of 206 of 20 Items

Question
What type of number will result from 3.4059...−85
?(1 point)
Responses

Irrational, because both numbers are irrational.
Irrational, because both numbers are irrational. - no response given

Irrational, because one number is irrational.
Irrational, because one number is irrational. - no response given

Rational, because one number is rational.
Rational, because one number is rational. - no response given

Rational, because both numbers are rational.
Rational, because both numbers are rational. - incorrect
Incorrect

While repeating decimals are rational, those without a repeating pattern are not.
Remaining Attempts : 2

1 answer

To determine the type of number that results from the expression \( 3.4059... - 85 \), we first need to classify the numbers involved.

  1. Identify the nature of the numbers:

    • \( 3.4059... \) is a repeating decimal. This means it can be expressed as a fraction and is, therefore, a rational number.
    • \( 85 \) is an integer, which is also a rational number because any integer can be expressed as a fraction (e.g., \( 85 = \frac{85}{1} \)).

  2. Perform the operation:

    • Since both \( 3.4059... \) and \( 85\) are rational numbers, the result of their subtraction will also be rational.

  3. Conclusion:

    • The result \( 3.4059... - 85 \) is a rational number because both numbers involved in the operation are rational.

Based on this analysis, the correct response would be:

Rational, because one number is rational.

This is true because both numbers are rational, making any operation (addition or subtraction) between them also yield a rational result. The confusion in the question lies in the phrasing; the answer reflects that, while only one number needs to be rational for the result to be rational, in this case, both numbers are rational.